**We study the phenomenology and develop the microscopic theory of non-linearly driven, many-body localised systems. We analyze the linear response of far off-equilibrium steady states in quantum magnets as a means to probe and characterize many-body localization. Moreover, we investigate how the physical properties of the low temperature state of these systems depends on the annealing protocol and the strength of the coupling of the magnetic system to a phonon bath, and how the latter might be used to engineer interesting entanglement properties.**

Localisation in quantum systems remains both fundamental to science as well as technology. It is an old subject, starting with the work of Anderson [1], whose name is associated with disorder-induced localisation - and Mott who predicted a localisation transition [2] due to the repulsion between electrons. The combined problem of many-body localisation persists to this day, despite considerable recent theoretical progress. Over the last few years, the problem has acquired practical relevance for systems of quantum devices, most notably the "D-wave" processor which attempts to implement adiabatic quantum computation, whose utility as a matter of principle may be limited by localisation effects [3]. Indeed, such effects may impede the adiabatic adjustment of the system ground state, as well as finite temperature thermalisation. However, from an opposite point of view, this is a highly desired effect: Interacting but nevertheless localised systems constitute promising platforms for the quantum information processing of coherent, spatially localised degrees of freedom in thermodynamically large systems. [4]

In the theoretical part of this project we study the phenomenology and develop the microscopic theory of non-linearly driven, many-body localised quantum magnets. We analyze the linear response of far off-equilibrium steady states as a means to probe and characterize many-body localization. These insights will be used to analyze and interpet neutron and X-ray scattering measurements that yield space- and time-dependent spin correlation functions, also in the presence of the AC drive fields that can burn spectral holes. The combination of these efforts is expected to provide an understanding of hole-burning and the emergence of quantum coherence in quantum magnets and advance the understanding of many-body localisation in general.

A further goal of the theoretical part of this project is to understand the coexistence of very different states of matter in the very same material, which arise due to a different coupling strength to the phonon heat bath. It is of fundamental interest to understand the evolution of quantum entanglement in the system as it is thermally annealed in the presence of a weak or strongly coupled heat bath. Recent experiments suggest that the latter strongly influence the entanglement in the resulting states of the quantum magnet, as reflected by their entirely different response to driving. This opens the possibility to use the coupling to a bath as a knob to engineer quantum states of desired properties.

[1] P. W. Anderson, Phys. Rev. 109, 1492 (1958).

[2] N. F. Mott, Proc. Phys. Soc. (London) A62, 416 (1949).

[3] B. Altshuler, H. Krovi, and J. Roland, Proc. Natl. Acad. Sci. USA, 107, 12446, (2010).

[4] R. Nandkishore and D. A. Huse, Ann. Rev. Cond. Matt. 6, 15 (2015).